I had heard that contrary to some stereotypes, autism and schizophrenia are not associated with higher intelligence; and a bit of checking on Google Scholar seems to confirm that mental disorders are usually associated with lower intelligence:

http://archpsyc.jamanetwork.com/article.aspx?articleid=481989#qundefined :

There was no association between premorbid IQ score and risk of bipolar disorder. Lower IQ was associated with increased risk of schizophrenia, severe depression, and other nonaffective psychoses.

http://bjp.rcpsych.org/content/187/5/407.short

Schizophrenia and related disorders, other psychotic disorders, adjustment, personality, alcohol and substance-use-related disorders were significantly associated with low IQ scores, but this association remained significant for the four non-psychotic disorders only when adjusting for comorbid diagnoses. For most diagnostic categories, test scores were positively associated with the length of the interval between testing and first admission. ICD mood disorders as well as neuroses and related disorders were not significantly associated with low IQ scores.

For OCD I've seen some results suggesting there was a link, and other suggesting there wasn't.

I've seen a few studies talking about association of mental illnesses with crime and violence, though it doesn't seem clear whether it's because of the mental illness or because of low intelligence, poverty or substance abuse who tend to be associated with mental illness.

For example, http://archpsyc.jamanetwork.com/article.aspx?articleid=495755#qundefined

Studies of criminality among patients in psychiatric hospitals and of mental disorder among incarcerated offenders have suggested an association between the major mental disorders (schizophrenia and major affective disorders) and crime. However, these investigations are characterized by notable methodological weaknesses, and, consequently, this conclusion has remained tentative. Little is known about the criminality of intellectually handicapped people. The present study examined the relationship between crime and mental disorder and crime and intellectual deficiency in an unselected Swedish birth cohort followed up to age 30 years. It was found that men with major mental disorders were 21/2 times more likely than men with no disorder or handicap to be registered for a criminal offense and four times more likely to be registered for a violent offense. Women with major disorders were five times more likely than women with no disorder or handicap to be registered for an offense and 27 times more likely to be registered for a violent offense. These subjects committed many serious offenses throughout their lives. The criminal behavior in over half these cases appeared before the age of 18 years. Intellectually handicapped men were three times more likely to offend than men with no disorder or handicap and five times more likely to commit a violent offense. Intellectually handicapped women were almost four times more likely to offend than women with no disorder or handicap and 25 times more likely to commit a violent offense. The results of this investigation confirm and extend previous findings indicating that individuals with major mental disorders and those with intellectual handicaps are at increased risk for offending and for violent offending.